jgreenfield@seol.net.au wrote:

PD wrote:

jgreenfield@seol.net.au wrote:

PD wrote:

jgreenfield@seol.net.au wrote:

PD wrote:

jgreenfield@seol.net.au wrote:

PD wrote:

jgreenfield@seol.net.au wrote:

PD wrote:

jgreenfield@seol.net.au wrote:

PD wrote:

jgreenfield@seol.net.au wrote:

Starbles@Earthlink.net wrote:

Which infinity? Positive or negative infinity?

Let's say that 1/0 = 1/x, and infinity is lnx. If 1/0 = infinity, then
1 = 0 times infinity. But x * lnx as x approaches infinity is zero.

How does your notion of infinity square with that?

There is *nothing* "less than" zero. There is NO physical entity which
is less than zero. Such a description (read name) for less than zero,
is never a reality- always just a human invention of the mind. When a
situation arises that calculation has produced a net negative, then a
mistake has been made in the math (it may be faulty), or the assumption
upon which the calculations depended (position of the zero coordinate),
was wrong/mistaken.

Jim G
c'=c+v

I can think of two quantities, both of which have nonzero (and
opposite) effect in nature, but the sum of which is zero effect in
nature. How would *you* characterize those quantities?

Don't be coy! What are they? After all, I have promised to do a thread
featuring my bare arse, if one is ACTUALLY a "less than zero physical
entity"

Before I give a couple of examples, the question was how you would
characterize those quantities. The way I see it, there are two ways to
characterize them:
1. As 1-D vector quantities, both with nonzero magnitude, but pointing
in the opposite direction.
2. As scalars on the real number line, one positive and one negative.

Note that I am asking for a *mathematical* characterization of the
*quantities*, so that we can have an operational definition.

The next question I would ask you is whether you think there is a
clear, fundamental distinction between those two characterizations. If
there is, what is it?

Wising up? at least you haven't mentioned money, electrons et al......

The "math characterisation" is the root of the problem. Addition is
accepted when it suits, but seen to be lacking when a positional
description, rather than a "less than" is involved. eg distance from A
(-1) to B (+1) is NOT zero.
Yet (-1)+(+1)=0 otherwise.
Similarly, the vectors cancelling look fine, until they represent
SOMETHING eg
forces (the rope gets broken- the forces didn't cancel).

Well, then I'd say one has to be a bit more precise in defining terms.
Position is not the same thing as, say, displacement. The
*displacement* from A to B in your example above is indeed 2, and the
displacement is given consistently by (final position) - (initial
position) = 1 - (-1) = 2.

Now, suppose I say that I want to know the displacement from the origin
O (position=0) to A. Following the above prescription, then we might
say the displacement is (-1) - (0) = -1. No, no, no, you might say, the
distance gone is obviously 1, not -1! So true, I might say, but I am
referring to displacement, not distance.

The problem clarifies if I ask what is the displacement from O to B if
I first go from O to A and then A to B. I need to be able to combine
the displacements in such a way that it's clear that if I go from O to
B or from O to A to B, I still end up at the same place. But if I go
from O to A and say that is 1 and from A to B and say that's 2, then if
I combine those to get 3, then I'm obviously not getting what I'm
looking for, because if I go from O to B directly, I get 1. In this
way, combining displacements does a much better job than combining
distances.

No problem, you might say, we'll just use + sometimes for combining
distances and - sometimes, depending on the direction. And I say then,
why? Why, when displacements contain the same information and the rule
for combination is then always +?

The difference, you might say, is that there is physics content in
using positive distances, and keeping track of + and - in the
combinations is just the work we have to do in the math to keep it all
straight, and putting the signs in the distances to make them
displacements confuses math and physics. And in response, I would
politely disagree and say that it's *all* mathematical convention, a
model we use to accurately predict nature, and I like how my model
works better.

PD

I learned this stuff way back- George D has given me a reefresher
lately, very similar to your explanation. The FACT remains, that as
handy as it may be to use "displacement" as exampled above, REAL
physics would see you run out of fuel 1/3 of the trip--
anywhere from point 0 is positive, when considering distance, time
taken, fuel required, or any other real-world exercise. The "where I
am" may be important, but the "what I need to get there" is not to be
ignored.

I jumped off this a little too quickly. The point I was trying to make
is the distinction between displacement and distance. Distance is the
ground covered along the path. Displacement is *where you are* relative
to where you began. Obviously, distance going from O to A to B is
different than the distance from O to B, but the displacement is -- and
should be -- independent of the path.

Ref the 727, I would calculate the time taken for the flight using REAL
additions of velocities, and knowing fuel consumption per time (nb
unalterable time; not that flexible crap), perfectly calculate time for
journey, and fuel needed.

1. Note that the distance covered is not the airspeed times the time.
Thus your contention that I need to do everything by *distance* and not
displacement seems to have an exception here by your own admission.

Nope. I use the GPS AND the airspeed.

Really? Explain how. Take some sample numbers for the quantities
mentioned and show how.

That merely takes us down the road where you outright reject addition
of velocities other than per AE, so I am not bothering to go down there
yet again.

No, I'm more interested in how you do this without negative numbers, or
how you choose whether to add or subtract positive numbers in a
case-independent way. I'm perfectly willing, for the case indicated, to
use the approximation of algebraic addition of velocities. So do it,
using the GPS and the airspeed, as you indicated.

2. I wonder how it is you *know* that your version of addition of
velocities is the REAL addition of velocities.

I only use these assumptions; that 1+1 = 2 a+a = 2a and
c+c = 2c

I don't know why you think velocities add this way. Moles of compounds
don't. Vectors don't. Rotations don't.

As above

The question was how you *know*. Any acceptance or rejection of that
model for adding velocities ought to be based on experimental
confirmation, don't you think?

It is the greatest con-trick since certain religious beliefs took hold,
to suggest otherwise.

I also agree with Don S vectors for forces, and I DRAW and
MEASURE to get the outcome of the net force and direction thereof

This will work, if this is how you want to do it. It has a few
problems:
1. It will not reflect the precision of the inputs if the input values
have greater than three digit precision, unless you want to make a
*large* picture.

Larger the better!

Well, then by golly, you stick to your newsprint and crayons and have
at it!

It may be beyond (read is likely to remain so ) our computing powers,
but that is NOT a reason to accept a wrong result, for the only reason,
that to pursue the correct one is "too hard".

Again, I'll ask you how you know the algebraic result is a wrong
result.

2. It's hard to do for vectors that span more than two dimensions,
unless you want to make a 3D model to generate every answer.

Sure it's "hard"! That is why FoRs have become so entrenched in the
math and physics, that they are accepted as having some significance.
ALL for's are, are a means of avoiding the difficulties of working with
complex dynamics
eg we can't calculate positions accurately when a depends on what b is
doing, which in turn depends on c etc. Just considering a,b then b,c
is EASY, and the "math" for changing the frames is supposed to solve
the problem. The drawback being, that as c'=c+v the results are WRONG.

Really? What evidence do you have for that?

velocity (read c) = frequency x wavelength

OK, so all we really need to do is to *measure* the frequency and the
wavelength from a moving source to find out if the product is c or c',

right? Or would you maintain that *even if the product of the measured
values* was c and not c', there would *still* be no reason for one to
change to make the product c. In other words, what experimental
evidence is required for you to consider that you've made a mistaken
presumption?

Variations to observed f (or u if that is what is being measured) are
observed from every moving (ref us) source in space, and there is NO
PHYSICAL REASON why the other changes magically to present c.
(No reply required-- I am not into discussing any more magic on these
threads)

3. It's hard to do for general cases (algebra and variables and all)
unless you want to take five or more numerical examples for every
single general case to try to determine some trend.

Yep, but why get wrong answers, because the alternative is TOO HARD?

Really? What evidence do you have that the answers are wrong?

3^2 = 3+3+3=9
300,000+300,000+300,000........(300,000 times) ie c^2 DOESN'T
=9x10^10
according to SR

Well, *that's* patently not true.
In SR, c^2=(3.0E8 m/s)^2=(300,000,000 m/s)(3,000,000 m/s)=9.0E16
m^2/s^2,
and I don't have any idea where you got the idea it wasn't so in SR.

The question is what *experimental evidence* do you have that adding
velocities like
(v1+v2)/(1 + v1*v2/c^2) is a wrong result?

Writing down what you think it *should be* theoretically (i.e. v1 + v2)
is not evidence that the other is a *wrong* result. Right and wrong is
determined by comparision with nature, and nothing else.

Then again, you only accept 3^2 = 9 for the imaginary; for realities
such as mass or distance, you reject it

Be my guest if you don't want to use signed numbers to do calculations
in physics because you think that signed numbers don't represent
physical reality. You have much fewer resources available to do
calculations as a result, but that's certainly your perogative.

Build bigger computers (number crunchers).........at least the answer
will come out right.

Ah, but bigger computers don't draw and measure, or build 3D models to
add vectors in more than 2 dimensions. They used signed numbers. So
computers are out...

Nope! The atoms in the silicon chips are either ON or OFF; they do NOT
have three options.
This is equivalent to 1 , 0 (I don't care if you use the "name"
-1 , 0 but there is NOT
-1, 0, +1 That is only the math of the computer language, not
the physical operation of the machine

Yup. And they use one of those bits in a string of bits to keep track
of sign. Would you like a reference about this?
Moreover, this doesn't change the fact that computers don't draw and
measure, and they don't build 3D models.
So how again are you going to use computers to combine positive-only
physical numbers and keep track of whether to add or subtract them?

Your argument at this point seems to be "Yes, but only distance matters
physically, and displacement does not." This I can argue is not the
case, and I think you would agree with that even before I made such an
argument. My airplane example in my other reply is an indirect example
of that.

Knowing my travel history, time, speed, and directions, I can perfectly
well determine my final displacement, AND plan my fuel requirement.
some joker in another thread says he doesn't care for the journey, just
his arrival point, as per your contention. The joke will be on us, when
he plans a highway with no service stations, on the assumption that we
all make the return trip.

There are cases where the journey is not relevant to the answer.

Father: " Son, have you used the car".
Son: "No Dad, its still in the shed"
F " Well how come it is out of petrol"?

I'll give you an example, since you seem to be obsessed on
distance-dependent parameters, rather than displacement-dependent
parameters.
A climber with a leaky lung encounters some chest pain at 14,500 ft.
elevation. He's advised by a doctor that he'll feel better and the lung
will reinflate if he can get to 10,500 ft. There's a camp (at B)
downhill from the summit (at O) that satisfies that altitude
requirement. It will make no difference whether he proceeds by the easy
but longer trail from O to A to B, or whether he proceeds by the
shorter but steeper trail directly from O to B.

Another example:
A car battery sets up a voltage difference between its terminals,
marked O and B. There are two resistive paths through wires, run in
parallel, between these two terminals. One path runs through the
starter, one path runs through the headlights and dashboard panel
lights and taillights. The voltage at B will be the same whether one
starts at O and goes straight thruogh the starter to B, or whether you
go through the longer, more tortuous path through A on the way to B.

All good, but when the history (how the displacement occurred) is
forgotten, wrong conclusions may be drawn

Maybe, maybe not. There are some things that don't depend on the
journey.

As illustrated above in a couple of homegrown examples.

So I say use (-) to describe a position or direction; use it to show
reduction (less than an equal or greater positive).
When a net result of a calculation yields "less than zero", either a
mistake has been made by using both systems in the same
derivation/calculation, or a WRONGFUL assumption has been used (eg
Schwartz claimed -300K; if such a temperature was found, I suggest that
it was NOT less than zero temp, but that -273K needs to be revised as
being zero temp/heat.

I know of no physical state with a temperature of -273K (aside from the
fake temperature associated with the inversion present in lasing).

It wouldn't be the first fake pulled by Al S.
Now what about the fake reversal of direction of the train in the LT's,
which is necessary to "show" the contraction??

Response?

Now why would I want to wander down an irrelevant tangent, let alone
one so vaguely expressed? If you want to start a new topic, start one.

You introduced "displacement"; the displacement in question being the
ends of the train, and how they come to be at different coordinates
when considered jointly, than singularly.

The displacement in question was not the ends of the train. Where in
our conversation did "train" come up?

Where I mentioned the LTs (for length contraction)

Ah, so it was YOU that brought it up after all. If you want to start a
new topic, start one.

NB: "less than zero physical entity"- not matheramagics
(...anything in energy? force? distance? time? mass? )
(and the point being that the LT's, by reversing the direction of the
train/light during the "proof" of the postulate of length contraction
are faulty/fraudulent)

.....and still only math dogma! WHERE are these physical entities you
have promised?

Well, let's see. I mentioned charge and how to calculate the force
between two charges. You haven't addressed that one.

equal forces in opposite directions yeilds no net MOTION
If particle a exerts -1 left, particle b +1 right net force
between the particles is +2

Well, that's funny how you calculated that in the first place. Let's go
back to simple Newtonian physics for a while, shall we? Or do you not
believe in Newtonian physics, either?

Make up your mind; are you arguing physics or math (as in ZZ
engineering)-
I am STILL awaiting "less than zero" physical entities.

(if you think there is NO force between them, they should be VERY easy
to pull apart.

But how about another? I have two varying forces acting in the same
direction on an buoy, both of which vary periodically (sinusoidally)
with time but with different frequencies.
F1=(20 N)sin(3.2t + 5)
F2=(5 N)sin(6t - 4)
and I need to make an active correction piston on the other side of the
piston so that the net force is zero and the buoy does not accelerate.
I suspect that the force due to that piston is probably sinusoidal
also. How would *you* go about characterizing these three forces and
combining them so the result is zero?

Not the point. The total energy/forces applied will need to DOUBLE, not
cancel to zero
(My brother-in-law had a similar problem with his drilling rig, which
swayed due to a transveresly mounted pump. He managed finally to
counter-weight the flywheel to negate the pulses of material being sent
in one direction, and the reversing piston directions. Dunno how he
managed it, but sure as hell there were still forces acting)

Right, and that's the point. It's possible to have two *nonzero*
quantities combining (summing) to add to a zero sum. How would you
characterize the nonzero quantities that sum to zero?

By direction, and magnitude.

OK, so you want to represent them as 1D vectors, rather than signed
numbers.
Now, I'll ask you, what is the mathematical distinction between
tracking the direction of a 1D vector and tracking its sign? That is,
if I mark "this way" as being a + number and "the other way" as being a
- number, what differences do you have between the two methods and the
physical interpretation thereof?

Now suppose you have two numbers that combine not as the sum but as the
product.
E.g. Coulomb's law says that the force between two charged objects with
charges q1 and q2 has the same magnitude for each object and is
proportional to q1*q2. Note that if we use two protons (or two
balloons), the force is mutually repulsive but it still is proportional
to the *product* q1*q2. Now if we only change *one* of the charges to
an electron (or from a balloon to the hair that I rubbed the balloon
on), then the force remains the same in magnitude, but the force has
changed direction to be attractive rather than repulsive. Now, in this
case, how would *you* characterize the numbers that quantify the
charges, in a completely positive-only sense, such that this behavior
is correctly modeled?

If they cancel, no net motion.
But this is where the HISTORY is important. If someone comes across a
rope between two objects, he has no idea what will happen when he cuts
rope. If he knows the HISTORY, ie how much tension/force/work was
applied to the system in the past, he can accurately predict the
outcome of cutting. Otherwise he sees nothing happening, assumes zero,
and may get a surprise. He needs the history to know if forces are
cancelling , or were never applied.
(and don't forget time; that has no negative "less than zero" either,
and the return trip will ALWAYS be the sum of two positives, no matter
where a journey ends.)

Jim G
c'=c+v